Is it viable to write a story taking place in four spatial dimensions?

[Wayne Mack]

But the fact that we do move through time, means (in my opinion) that it is a dimension. When we look up at the sky, the stars we see no longer occupy the particular place in time that we see; some no longer exist at all. They occupy (or occupied) a spacial position at a point in time. Not quite the same thing, but calculating a ship's position required knowledge of longitude, which was impossible to do without knowing the precise time of day.

We know that time is not a constant, and it is quite possible at some point we may have more control over how we travel through it, as we do with the other 3 dimensions. Certainly any story that deals with time travel (in my opinion) deals with movement in the fourth dimension, but just because we don't currently have much control with how we move through it (as also with many scifi stories such as Quantum Leap), doen't mean that it doesn't exist.

@paranoid marvin Very true, but in our current 3D reality, we can't travel in the full dimension of time.
We can move up and dome. Left and right. Forward and backward. But being 3D, we can only move in one direction of time, that happens to be future.

I have found it better to use spherical coordinates rather than cartesian. In standard space, this avoids the nasty concept of negative distance (and negative velocity and negative acceleration). In spherical coordinates, there is one vector with a linear distance from the origin. The other dimensions are degrees of rotation in a horizontal plane and in a vertical plane. From any arbitrary point, one can move to any other point by travelling a positive distance. Time would also be a vector with only a positive direction of travel.

 

[Wayne Mack]

I would assume that the people in a four dimensional universe would live on a planet that is a four dimensional sphere. On a two dimensional planet, i.e., a circle, people would normally live in a bent one dimensional world, unless they expended energy to overcome gravity and move to a higher level. On a three dimensional planet, i.e., a sphere, people live in a bent two dimensional surface, unless they expend energy to overcome gravity and move above the surface. For a four dimensional planet, this extrapolates to people living in a bent three dimensional sphere, unless they expend energy to overcome gravity and move out of the sphere. I'm not sure how to picture this.

The writing challenge, which has been touched on in some previous comments is, how does one make this setting significant to the plot? It does no good to introduce a gee-whiz setting, if the plot could just have easily taken place in the current world.

 

[Swank]

I'm not sure how to picture this.

If anyone can, those three people will buy the OP's book.

 

[farntfar]

We can move up and dome. Left and right. Forward and backward. But being 3D, we can only move in one direction of time, that happens to be future. And yes, movement through time requires movement through 3D space. Thus, for me, proof that time in its fullness of future, present and past, is a true physical dimension at right angles to each of the 3 that we do have control of. If you get what I'm saying...

So one of the first questions to resolve is what you're going to call up and down (or left and right, or forward and backward) in the fourth dimension.
It has to be something that sounds and feels right. Calling it +i and -i may solve the physis, but it's never going feel real to say, "Bill walked three metres to the -i" or "Othello exits stage i".

I say this because, as a reader, if it's going to grab my attention you can stuff the physics (*). It's whether it feel natural that will mean I continue reading.

*As interesting as that may be to another part of me.

 

[paranoid marvin]

"Have you ever thought what it's like to be wanderers in the fourth dimension? Well, have you?" Doctor Who.


*points at 2 boxes, smaller one closer, larger one further away*

"Which box is larger?"

*points at one further away* "That one."

"But it looks smaller."

"Well, that's because it's further away."

"Exactly. If you keep that exactly that distance away, and have it here, the large one would fit inside the small one."

"That's silly."

"That's trans-dimensional engineering."

 

[THX1138]

@farntfar That is why as writers we need to write 4D in a 3D view with that one or two '4D quirks' (theoretical or made up) to make the 4thD seem real to the readers, other than the time travel stuff. As you know.

@paranoid marvin it's a matter of quantum perspective. Who knew!

 

[Astro Pen]

I'm thinking directions of escape for some reason. Particularly through dreamscapes, which never have much time for logical physics. You sort of wormhole about through the other 3 dimensions in ways that looks impossible when awake.
Up, Down
Left, Right
In, Out
Flow, Lock

Yeah, I could 'flow' from any 3d situation, or 'lock' into it if wanted to

 

[Serendipity]

Of course, hyperspace is the fourth spatial dimension that lets spacecraft travel faster than light from one point in our 3-D universe to another.

... well, it's one of the standard definitions of hyperspace.

 

[Biskit]

And yeah, it will be complex, although you don't have to specify all the laws of physics of a universe 100% to write a story.

I think you need to pick out a few significant ones though, and the fact that you're picking 4-D for the space tessellation suggests that obvious "macroscopic" ones such as E-M wave propagation and atomic packing ought to be addressed. Is your universe going to treat the equivalent of light as having a constant speed? If not, then that would have huge consequences. If atoms pack differently, the properties of solid materials will be seriously different. I'm resisting the urge to try to figure out what basic quantum mechanics would look like if re-cast in 4 dimensions.

As others have said, you probably don't want to focus too much on the physics, but my feeling is that you ought to select two or three "big things" and pick a behaviour that suits your story, because trying to work out what might really happen is challenging to say the least. Tiny details can have startling consequences, such as adding tiny impurities to silicon having a radical impact on the electrical properties. (If your atoms in 4 dimensions pack differently to 3 dimensions, then bulk electrical properties will also change. )

Now, have you thought about the chemistry of 4-dimensional atoms?

Of course, we might already be living in 4 spatial dimensions, but only know about 3 because light doesn't use number 4...

 

[Biskit]

I say this because, as a reader, if it's going to grab my attention you can stuff the physics

I'm sorry, but at this time of year you should only be stuffing a turkey. Leave the physics alone.

 

[sinister42]

This actually sounds like a fascinating concept. I think it's absolutely doable. I have no idea how, but I look forward to reading it.

 

[farntfar]

Oh! It is doable.
I know lots of people who stuff turkeys at this time of year. Some even stuff geese.

 

[Biskit]

Some even stuff geese.

Been there, done that, got feathers everywhere.

This year we're having peanut curry - it turns out that peanuts (generally) don't fight back the way a goose** does, nor leave piles of poo to be cleaned up.

**Also, Idris and Chocky now live over in East Cornwall.

 

[Serendipity]

For those of you interested in shapes in four spatial dimensions, and in particular, polygons...

In 2 spatial dimensions we have: No. of corners = No. of sides

In 3 spatial dimensions we have: No. of lines + 2 = No. of sides + no. of corners

From having a little play around with four dimensional shapes I would conjecture that:

No. of lines + No. of Volumes = No. of surfaces + No. of corners

So when you are considering describing four-dimensional shapes that have flat surfaces you may wish to use the above simple formula to check that they could exist in four spatial dimensions.

 

[sknox]

It's interesting as a concept mainly because we're usually in three dimensions. So it's novel (pun unavoidable). But is it important?

Consider that we have lots and lots and lots of books in which no one even begins to mention the fact that all the characters in it are living in a three-dimensional world. They can have romances, adventures, solve mysteries, or go off on long philosophical jaunts, all without once needing to explain to the reader that this is all happening in a three-dimensional world.

So, a 4D setting only matters if four-dimensionality matters to the story, that is to the characters in the story.

You mentioned that your story has people who live in three dimensions but find themselves transported or warped into the 4D world. Are they trying to get "back"? Is there an invasion planned? A murder took place? A kingdom that needs saving?

It could also be a story where some stuff happens, but it happens to happen in a 4D setting. How would something ordinary, saving the cat, be different in four dimensions?

I think you can just make up whatever characteristic(s) you want for the fourth dimension, then construct a story that takes advantage of one or more of those attributes. Maybe borrow ideas, from quantum physics, which as the temerity to suggest ten or more dimensions without bothering to explain them in mortal terms.

 

[Dave]

How would something ordinary, saving the cat, be different in four dimensions?

There are bottlenecks in our 3D world that might be avoided i.e. the cat can walk through walls. Also, the cat might die of old age, but accidents to the cat might be avoided by the revision of events.

 

[THX1138]

Been there, done that, got feathers everywhere.

This year we're having peanut curry - it turns out that peanuts (generally) don't fight back the way a goose** does, nor leave piles of poo to be cleaned up.

View attachment 113615

**Also, Idris and Chocky now live over in East Cornwall.

Where 's the cat? Nice healthy geese though!

 

[Swank]

There are bottlenecks in our 3D world that might be avoided i.e. the cat can walk through walls. Also, the cat might die of old age, but accidents to the cat might be avoided by the revision of events.

That sounds like great fiction, where nothing will happen to the cat and there is no dilemma to solve.

 

[Dave]

That sounds like great fiction, where nothing will happen to the cat and there is no dilemma to solve.

Maybe it's only possible to revise events nine times due to some fundamental Law of Physics?

 

[Biskit]

Where 's the cat? Nice healthy geese though!

All of the cats have more sense than to hang out anywhere near the geese, or the sheep, or the chickens...